What does a steady rate compound to, gained or lost?
Multiples of the starting balance for rates held perfectly steady: arithmetic on assumptions, not typical returns.
| Assumed path | 12 months | 24 months | 60 months |
|---|---|---|---|
| +1% every month | ×1.13 | ×1.27 | ×1.82 |
| +2% every month | ×1.27 | ×1.61 | ×3.28 |
| +2%, every 4th month −3% | ×1.09 | ×1.19 | ×1.54 |
| −1% every month | ×0.89 | ×0.79 | ×0.55 |
| −2% every month | ×0.78 | ×0.62 | ×0.30 |
Why the losing rows are here
Multiples of the starting balance for rates held perfectly steady. These are arithmetic on assumptions, not expected or typical returns: no trading record moves by the same percentage every month, and the losing rows compound just as hard as the winning ones.
Why do a few losing months cost so much growth?
Six −3% months out of 24 turn ×1.61 into ×1.19; each loss needs a larger gain to undo it.
| Loss | Gain needed to get back |
|---|---|
| −3% | +3.09% |
| −5% | +5.26% |
| −10% | +11.11% |
| −20% | +25.00% |
| −30% | +42.86% |
| −50% | +100.00% |
The default example in dollars
Because a loss shrinks the base and the recovery has to be earned on the smaller base. In the default example, six −3% months out of 24 turn ×1.61 into ×1.19: $10,000.00 ends at $11,896.89 instead of $16,084.37. Each loss needs a larger gain to undo it, and the gap widens fast as losses deepen.
The drawdown recovery calculator gives the same asymmetry for any loss.
Is the average return the same as the compounded return?
No: +10% then −10% averages 0% but ends at ×0.99.
Why the plain average overstates growth
Whenever returns vary, the plain average is higher than the rate the balance actually compounds at. +10% followed by −10% averages 0%, but the balance ends at ×0.99, 1% lower. In the default example the plain average is 0.75% a month while the balance grows 0.73% a month compounded. The more returns swing, the wider that gap gets. To see returns that vary from path to path rather than one smooth line, use the Monte Carlo trading simulator.
How much does taking money out change the result?
$100 out at the end of every month leaves $9,333.89 after 24 months in the default example.
Withdrawals stop compounding
A withdrawal no longer compounds. In the default example, taking $100 at the end of every month leaves $9,333.89 after 24 months, with $2,400.00 withdrawn. If the withdrawals are larger than the path can support, the calculator shows the period in which the balance runs out.
What does this calculator not tell you?
What any strategy, account or product will return.
Why a steady rate is not a target
It does not estimate what any strategy, account or product will return, and a steady percentage should not be used as a target to size trades against. Real results come in a varying order, with losing streaks that can be longer and deeper than a fixed pattern; sizing up to reach a compounding goal raises the chance of a deep drawdown. The risk of ruin calculator shows how position size changes the odds of reaching a loss threshold.